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Euler–Maruyama against the exact solution

Both paths use the same Brownian increments. Fewer steps means a cruder Euler path; the error plot shows how fast it vanishes as the step shrinks.

Parameters

Euler steps (n)8

28

Drift (μ)0.08

-0.30.3

Volatility (σ)0.40

0.10.8

Random seed: 7

Metrics

Error at T (this path)

4.36

Strong order (slope)

0.48

Weak order (slope)

1.00

One path, exact and Euler with n = 8 steps

Exact solutionEuler–Maruyama

Error against step size (log-log)

Strong error E|S_T − S̃_T|Weak error |E S_T − E S̃_T|Slope ½Slope 1Current n